@Carl Love 

Great work from a great person !

Thanks a lot ... :)

@Carl Love 

Dear Carl Love,

Thanks for your great commands .. You have almost answered my question, but the animation needs some adjustments! They should look like growing from 0% to 100% of their shape. Please, see the below animation effect of arbitrary 2D and 3D plots:

I. 1-dimensional plot:

f1 := (exp(-((1/15)*x)^10)-2*exp(-(x-Pi)^2))*cos(x)^2;

Then right-click and from 2-D plot select animated plot:

II. 2-dimensional plot:

restart; with(plots); animate(plot3d, [A*(abs(x)+abs(y))*exp(-sin(x^2)-sin(y^2)), x = -2*Pi .. 2*Pi, y = -2*Pi .. 2*Pi], A = 0 .. 1)

Again, your answer is awesome, and I hope to get the above small adjustments

Thanks again